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This engaging book offers an in-depth introduction to teaching mathematics through problem-solving, providing lessons and techniques that can be used in classrooms for both primary and lower secondary grades. Based on the innovative and successful Japanese approaches of Teaching Through Problem-solving (TTP) and Collaborative Lesson Research (CLR), renowned mathematics education scholar Akihiko Takahashi demonstrates how these teaching methods can be successfully adapted in schools outside of Japan.

TTP encourages students to try and solve a problem independently, rather than relying on the format of lectures and walkthroughs provided in classrooms across the world. Teaching Mathematics Through Problem-Solving gives educators the tools to restructure their lesson and curriculum design to make creative and adaptive problem-solving the main way students learn new procedures. Takahashi showcases TTP lessons for elementary and secondary classrooms, showing how teachers can create their own TTP lessons and units using techniques adapted from Japanese educators through CLR. Examples are discussed in relation to the Common Core State Standards, though the methods and lessons offered can be used in any country.

Teaching Mathematics Through Problem-Solving offers an innovative new approach to teaching mathematics written by a leading expert in Japanese mathematics education, suitable for pre-service and in-service primary and secondary math educators.

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This engaging book offers an in-depth introduction to teaching mathematics through problem-solving, providing lessons and techniques that can be used in classrooms for both primary and lower secondary grades. Based on the innovative and successful Japanese approaches of Teaching Through Problem-solving (TTP) and Collaborative Lesson Research (CLR), renowned mathematics education scholar Akihiko Takahashi demonstrates how these teaching methods can be successfully adapted in schools outside of Japan.

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Our summative tasks are divided into three classes - Novice, Apprentice and Expert. This is not a measurement of the difficulty of the content, but indicates the extent to which they require students to autonomously apply their mathematical knowledge: Novice tasks explicitly test particular items of content knowledge, Expert tasks are far less structured and require strategic problem-solving skills in addition to content knowledge. A “balanced diet” of Novice, Apprentice and Expert tasks is needed to properly assess the Mathematical Practices.

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The Maths4All project, funded by Science Foundation Ireland, has been running since 2019. Members of the DCU Institute of Education work in collaboration with teachers to run activities such as webinars and TeachMeets. Our main purpose is to create opportunities for teachers to share and discuss their practice and find ways to enhance their teaching of maths.

As of Spring 20222, we are also delighted to collaborate with Clare Education Centre and the the Teachers' Research Exchange to facilitate an online professional learning community.

The Maths4All website also presents high-quality activity plans, created for and with teachers, and video examples of mathematics teaching in Irish preschool and primary classrooms.

These activities were designed to align with the content of the draft specification of the new mathematics curriculum which was released for consultation in 2017/2018. The proposed curriculum suggests that the four elements of:

are central to mathematical learning. Each of the activity plans is structured to facilitate children's engagement with these processes and elements.

The video clips provide opportunities for teachers to see good practice in action and also to facilitate reflection on teacher practices that are relevant across all mathematics activities and all age groups. Professional development materials relating to the use of tasks and talk in mathematical activities are also provided.

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The Maths4All project, funded by Science Foundation Ireland, has been running since 2019. Members of the DCU Institute of Education work in collaboration with teachers to run activities such as webinars and TeachMeets. Our main purpose is to create opportunities for teachers to share and discuss their practice and find ways to enhance their teaching of maths.

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UCD Access and Life Long Learning Presentation

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UCD Access and Life Long Learning Presentation

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Pathways DEIS MATHS GROUP 9th May 2023 Final

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Welcome to my website. Hopefully you will find all the resources you need to help you in your study of Maths or Applied Maths. If you find any dead links, or any other issues, please contact me using the mail icon at the bottom of the page. Thank you. Joe

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Welcome to my website. Hopefully you will find all the resources you need to help you in your study of Maths or Applied Maths. If you find any dead links, or any other issues, please contact me using the mail icon at the bottom of the page. Thank you. Joe

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I first set up the Mr Barton Maths website back in 2007. If you find the website useful to help you teach or learn maths, please consider supporting my work by becoming a Patreon. Thanks so much!

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Today's mathematical research, both pure and applied, is paving the way for major scientific, engineering, and technological breakthroughs. Cutting-edge work in the mathematical sciences is responsible for advances in artificial intelligence, manufacturing, precision medicine, cybersecurity, and more. Find out how the mathematical sciences are helping to improve our everyday lives by checking out the stories and infographics below.
SCROLL DOWN TO LEARN MORE

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Illustrating the Impact of the Mathematical Sciences

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Today's mathematical research, both pure and applied , is paving the way for major scientific, engineering, and technological breakthroughs. Cutting-edge work in the mathematical sciences is responsible for advances in artificial intelligence, manufacturing, precision medicine, cybersecurity, and more. Find out how the mathematical sciences are helping to improve our everyday lives by checking out the stories and infographics below.

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arrow_back Back to Rich Tasks

Improving Learning in Mathematics (Standards Units) Rich Tasks

The "Improving Learning in Mathematics" (or Standards Units) resources are, in my opinion, some of the finest ever produced. They are rich, challenging, well thought-out and well resourced. In short, I love them.

From the NCETM website:

"This multi-media resource has been developed with teachers, trainers and managers. Improving Learning in Mathematics builds on existing successful practice and explores approaches that encourage a more active way of learning through the use of group work, discussion and open questioning. Learners are encouraged to 'have a go', become more independent and reflective about their mathematics, to learn to think mathematically rather than simply learning rules and most importantly, to enjoy their mathematics"

Mature_Maths_Trainee has kindly created and shared "classroom ready" versions of these outstanding resources, which not only save you a lot of time, but also contain tips, words or caution, and examples of students' work to help you have the most effective teaching and learning experience possible.

Below are the pdfs and PowerPoints of the main activities which I have found really engage and challenge my students. I would strongly recommend you give them a try!

Contents

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Standards Units Rich Tasks on Mr Barton Maths

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arrow_back Back to Rich Tasks Improving Learning in Mathematics (Standards Units) Rich Tasks The "Improving Learning in Mathematics" (or Standards Units) resources are, in my opinion, some of the finest ever produced. They are rich, challenging, well thought-out and well resourced. In short, I love them.

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See TTP in Action - The Lesson Study Group

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In this module, you will see how an experienced TTP practitioner plans and teaches a series of TTP lessons. Specifically, you will discover how the different instructional supports for a TTP lesson come together to build students' understanding of a particular mathematical topic: area of polygons.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children’s solutions,interactivities,games,articles.

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Prof. Takahashi teaches secondary students in Maynooth 2017

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Prof. Takahashi teaches secondary students in Maynooth 2017

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Another year and another brilliant Maths Counts Conference. A record crowd of close to 450 watched Professor Takahashi steer an open-ended path through geometry and then witnessed a first for Irish education as our amazing lesson-study teachers taught their students live for all to observe. If that wasn't enough, there were still 20 interactive workshops to choose from, a poster display of 52 lessons, an address by Maths Development Team National Coordinator, Dr. Anne Brosnan and a presentation on school self evaluation by Senior Inspector, Linda Ramsbottom. It's fair to say that everybody was tired but energised by conference end on Saturday afternoon.

Thanks to everyone who attended but most especially to our 250 lesson-study teachers and the students and staff of Maynooth Education Campus, Coláiste na hInse, Santa Sabina Dominican College and Temple Carrig School who gave up their weekend so that we all might learn some Maths.

Irish Maths Teachers Teaching Live

In a first for Ireland, Maths Counts saw Maths teachers teaching live lessons for all to see. If you missed out, we'll be posting videos of the full live lessons soon for everyone to view. In the meantime meet our live teachers and find out a little more about their lessons.

Team 1 - From Santa Sabina Dominican College, Sutton, Co. Dublin

Audrey Carty, Sandra Byrne, Claire Holton and Fiona McAvoy's lesson is The Polygon Predicament and is targeted at Leaving-Cert. Higher-Level students. Combining aspects of Geometry, Probability, Algebra and Functions this problem challenges students to make connections between the different strands of the Maths syllabus and aims to develop students' problem-solving skills, communication and ability to reason.

Team 2 - From Ballymakenny College, Drogheda & Coláiste na hInse, Bettystown

Catriona McArdle from Coláiste na hInse and Leona Matthews from Ballymakenny College worked across their schools to develop a lesson for first-year students. The Great Hall introduces students to algebra using structured problem-solving in such a way that students are encouraged to develop their algebraic reasoning skills, are motivated to engage with algebra and ultimately see algebra as sense making.

Team 3 - From Temple Carrig School, Greystones

Dr. Declan Cathcart, Deborah Crean, Nadia Douglas and Jill Condell's lesson Coordinate Geometry meets Synthetic Geometry is designed to help students to develop their deductive reasoning skills by devising as many solutions as they can to a geometric problem. Students are expected to draw on their knowledge of coordinate geometry and geometry theorems, corollaries and constructions to solve the problem. How did students approach the problem? What methods did they use?

You can find these and other lesson proposals in our Lesson Study Library.

Professor Akihiko Takahashi's Live Lessons

Professor Akihiko Takahashi wowed us for the second year running with his open-ended teaching of Geometry using structured problem solving. Professor Takahashi was ably assisted by first-year students from Maynooth Education Campus (incorporating Maynooth Post-Primary School and Maynooth Community College). Professor Takahashi also addressed the conference on the importance of open-ended tasks to maths lessons. You can download Professor Takahashi's lesson plan, with student worksheets included here and you can watch Professor Takahashi put the lesson plan into action in the videos below.

Dr. Anne Brosnan of the Maths Development Team gave a keynote address on the role that lesson study has played in supporting Irish teachers to incorporate structured problem solving into their Maths lessons. Dr. Brosnan outlined the growth of the Maths Development Team's lesson-study programme and how its continuation can propel Ireland to have world-class Maths education.

Interactive Workshops

Teachers who participated in Lesson Study 2016-2017 hosted interactive workshops where they gave audience members the chance to try out their problem-solving lesson, discussed their students' reaction to the lesson and discussed the many ways in which they benefited from being involved in lesson study. All the lesson proposals and problems presented during the workshops are available in our Lesson Study Library.

The 250+ Maths teachers who participated in Lesson Study 2016-2017 produced a total of 52 lesson proposals. The lesson proposals were summarised by 52 posters which were displayed throughout Maths Counts 2017. All 52 lesson proposals are available for download in our Lesson Study Library along with a PDF containing all the posters (large file - 300+MB).

Sponsors and Exhibitors

Thank you to our sponsors, Microsoft and Build-Up for sponsoring Maths Counts. Thank you to all our exhibitors who provided teachers with lots of useful information about the latest resources for teaching Maths.

Problem Solving Lesson Proposals

Check out the lesson proposals developed by Maths teachers involved in lesson study.

Search for a particular lesson or sort the lessons according to topic, year group or level.

Click RESET to return to the full list of lessons.

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PDST Post-Primary Maths | Maths Counts 2017

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Another year and another brilliant Maths Counts Conference. A record crowd of close to 450 watched Professor Takahashi steer an open-ended path through geometry and then witnessed a first for Irish education as our amazing lesson-study teachers taught their students live for all to observe.

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Prof. Takahashi teaching 1st years in Dublin 2016

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Prof. Takahashi teaching 1st years in Dublin 2016

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Maths featured prominently last weekend in UCD as 300 teachers and education professionals attended Maths Counts 2016. The conference focused on teaching through problem-solving and the role of Reflections on Practice in leading professional development in teaching.

Central to the conference was the work of teachers involved in Reflections on Practice. Thank you to the 25 teachers who presented their problem-solving lessons at the conference and to all those involved in Reflections on Practice throughout 2015-2016.

Thank you to our keynote speaker - Professor Akihiko Takahashi - who so brilliantly demonstrated the art of teaching through problem-solving. Professor Takahashi taught mathematics to a group of first-year students at the conference, and left us all with much food for thought in the approaches we use to teach mathematics. A special thank you to the students of Marian College and their teachers who participated so enthusiastically in the live lessons.

Thank you to all our sponsors: Microsoft, BuildUp, wriggle, IMLSN and The Ireland Funds and thank you to all our exhibitors who took the time to talk to teachers about all the invaluable resources which are available to enhance teaching and learning.

Professor Takahashi's Presentations

Here are the videos of Prof. Takahashi teaching through problem-solving and the lesson plans he used.

Participating Schools

A special thank you to all the teachers and schools who were involved in Reflections on Practice this year.

1. St. Michael's Secondary School, Finglas

2. Chanel College, Coolock Village, Malahide Road

3. St. Fintan's High School, Sutton

4. Fingal Adult & Further Education Ctr, Balbriggan

5. Deansrath Community College, Clondalkin

6. Coláiste Chú Chulainn, Dundalk

7. St. Fintina's Post Primary School, Enfield

8. St. Oliver's Community College, Drogheda

9. Drogheda Grammar School, Drogheda

10. Coláiste Bríde, Enniscorthy

11. Presentation College, Currylea, Tuam

12. Coláiste Cholmáin, Claremorris

13. Seamount College, Kinvara

14. Coláiste Iognáid S.J., Galway

15. Gairmscoil Einne, Inis Mór - Oileann Arann

16. St. Michael's College, Listowel

17. Coláiste Dún Iascaigh , Cashel Road, Cahir

18. Scoil Aireagail, Ballyhale, Kilkenny

19. Ramsgrange Community School, New Ross

20. Ardscoil Na Mara, Tramore

21. Rockwell College, Cashel

22. Christian Brothers School, Carrick On Suir

23. St. Mark's Community School, Tallaght

24. Coláiste Bhride, Clondalkin

25. John Scottus Secondary School, Donnybrook

1. Killinarden Community School, Tallaght

2. Holy Family Secondary School, Newbridge

3. Lucan Community College

4. Midleton College, Cork

5. St. Aloysius School, Cork

6. Our Lady's Secondary School, Castleblayney

7. Largy College, Clones

8. St. Tiernan's College, Crossmolina

9. Coláiste Mhuire, Tuar Mhic Éadaigh

10. St. Louis Secondary School, Kiltimagh

11. St. Leo's College, Carlow

12. St. Mary's Academy C.B.S., Carlow

13. Carndonagh Community School, Lifford

14. Errigal College, Letterkenny

15. Deele College, Raphoe

16. Loreto Community School, Milford

17. Pipers Hill College, Naas

18. Rathdown School, Glenageary, Dun Laoghaire

19. Dunshaughlin Community School

20. St. Flannan's College, Ennis

21. Glenstal Abbey School, Limerick

22. St. John Bosco Community College, Clare

23. Kilrush Community School, Clare

24. Children's Ark School, U.L. Hospital

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PDST Post-Primary Maths | Maths Counts 2016

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Maths featured prominently last weekend in UCD as 300 teachers and education professionals attended Maths Counts 2016. The conference focused on teaching through problem-solving and the role of Reflections on Practice in leading professional development in teaching. Central to the conference was the work of teachers involved in Reflections on Practice.

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Welcome

This site is being developed to support my Leaving Cert. Higher Level Mathematics students. The material is open for any student who finds the material helpful. Comments, corrections and recommendations are welcome.

Keep well and keep learning.

Best wishes
Mr. Roche

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This site is being developed to support my Leaving Cert. Higher Level Mathematics students. The material is open for any student who finds the material helpful. Comments, corrections and recommendations are welcome. Keep well and keep learning. Best wishes Mr. Roche

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PDST Post-Primary Maths | Leaving Certificate

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2D to 3D... That is the Question?
Students will be presented with a problem in which they need to select and use appropriate knowledge from the different strands in maths, and decipher ...

Prof. Takahashi's Lesson Proposal
Through a series of problems, students learn about the conditions required for congruency (includes student worksheets).

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PDST Post-Primary Maths | Lesson Study Library

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2D to 3D... That is the Question? Students will be presented with a problem in which they need to select and use appropriate knowledge from the different strands in maths, and decipher ... Prof. Takahashi's Lesson Proposal Through a series of problems, students learn about the conditions required for congruency (includes student worksheets).

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PDST Post-Primary Maths | Teaching and Learning Plans

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Mathematics Assessment Project - Lessons

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Mathematics Assessment Project - Lessons

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Classroom Challenges are lessons that support teachers in formative assessment. There are 100 lessons in total, 20 at each grade from 6 to 8 and 40 for 'Career and College Readiness' at High School Grades 9 and above. Some lessons are focused on developing math concepts, others on solving non-routine problems.

The Brief Guide for teachers and administrators (PDF) is recommended reading before using these lessons for the first time.

Each lesson is downloadable as an all-in-one PDF to print out, and a supporting PowerPoint presentation.

Finding a Lesson

There are several ways of navigating:

1. Use the menu on the left to browse by grade and topic area, or search for a key phrase.

2. Go to the Standards tab to find lessons linked to a particular content standard or practice.

3. The complete set of lessons is listed below in alphabetic order.

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Classroom Challenges are lessons that support teachers in formative assessment. There are 100 lessons in total, 20 at each grade from 6 to 8 and 40 for 'Career and College Readiness' at High School Grades 9 and above.

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Curriculum - Courses - Career

weusemaths.ie is presented by Dublin Institute for Advanced Studies and its aim is to showcase mathematics as a skill that is required for many rewarding careers. This website will link the current mathematics curriculum in Ireland to those who use the subject in their chosen career, along with presenting career pathways for students who have found a career they would like to pursue, but are unsure of what third level course they need to take. weusemaths.ie will link Curriculum - Courses - Career as well as informing you of public events and news that are maths related. Enjoy!

Career Sectors that use Mathematics

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weusemaths.ie is presented by Dublin Institute for Advanced Studies and its aim is to showcase mathematics as a skill that is required for many rewarding careers.

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UCD School of Mathematics and Statistics

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The School of Mathematics and Statistics, in conjunction with UCD Access & Lifelong Learning and the College of Science, runs a series of extra-curricular mathematics workshops for senior cycle post-primary pupils.

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https://www.ucd.ie/mathstat/rolemodelsinpstem/

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The 'Role Models in pSTEM: You can be what you can see' project was created to highlight positive role models for young women in the subjects of physics, mathematics, computer science and engineering. By creating videos for use in classrooms and on social media, the project hopes to make more young women aware of the very many career paths and opportunities available to them by pursuing these subjects. Following the UNESCO framework of factors influencing girls' and women's participation in STEM, the interviews explore the backgrounds and influences of each of the role models and highlight what they enjoy about what they do.

A handbook and slide deck are available for teachers to download and use in tandem with the videos.

Sharon Sweeney is a fashion designer who runs a small business that creates bespoke pieces that are ethical and sustainable - using organic, deadstock and recycled fabrics. At the National University of Ireland, Galway, she studied Environmental Science and worked in a lab for a short time before travelling to America where she studied part-time for a course in Fashion, and it was from that experience she realised her passion for design. She returned to Ireland and began studying part time for a diploma at the Grafton Academy of Fashion Design. She now draws from both her design and science background to not only create slow fashion, but also to create awareness around the damaging effects the fast fashion industry has on the environment.

NUALA CRIMMINS

Nuala Crimmins is a Partner in Grant Thornton Ireland, where she is Head of Insurance. Having studied Actuarial and Financial Studies in UCD, Nuala went on to work in a variety of roles across the insurance sector, in Ireland and internationally, spanning areas such as regulation, pricing & product development, project management and internal audit.
Project Leads:
Dr Aoibhinn Ní Shúilleabháin, UCD School of Mathematics & Statistics

Dr Catherine Mooney, UCD School of Computer Science
Project Funders:
HEA Gender Enhancement Fund

Institute of Physics
Project Partners:
WITS Women in Technology & Science

Irish Science Teachers Association

Irish Mathematics Teachers Association

Irish Applied Mathematics Teachers Association

Engineering & Technology Teachers Association

Institute of Guidance Counsellors

CESI (Computers in Education Society of Ireland)

Engineers Ireland

INGENIC Irish Network for Gender Equality in Computing

Third Level Computing Forum

Ireland ACM Special Interest Group on Computer Science Education

FutureNeuro the SFI Research Centre for Chronic and Rare Neurological Diseases

Videos created by: Stand Out Films
https://www.standoutfilms.ie/

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The 'Role Models in pSTEM: You can be what you can see' project was created to highlight positive role models for young women in the subjects of physics, mathematics, computer science and engineering.

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Leaving Certificate Videos

These videos were designed and produced by UCD Maths Support Centre tutors Rowland Bennett, Anthony Cronin, Kaitlin Farrell, Emma Howard, Christopher Kennedy and Aidan Long. The 235 videos cover both the Higher Level and Ordinary Level Leaving Certificate mathematics courses. They cover four strands of the Leaving Certificate mathematics curriculum:

These videos were made possible by the very generous funding of Citi Foundation with thanks to Jennifer Murphy and Fiona Swenney from the UCD Access and Lifelong Learning's Future You programme.

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These videos were designed and produced by UCD Maths Support Centre tutors Rowland Bennett, Anthony Cronin, Kaitlin Farrell, Emma Howard, Christopher Kennedy and Aidan Long. The 235 videos cover both the Higher Level and Ordinary Level Leaving Certificate mathematics courses.

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Vicky Neale is the Whitehead Lecturer in the Mathematical Institute in Oxford. As well as teaching undergraduates, her role involves discussing mathematics w…

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Women Who Figure - Spotlight exhibits at the UC Berkeley Library

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Hypatia of Alexandria
Hypatia of Alexandria
Greek mathematician, astronomer, and philosopher in 4th & 5th century Egypt, recognized for her commentaries on prominent mathematical works of her time

Book on Display:

Hypatia of Alexandria : mathematician and martyr / Michael A.B. Deakin
QA29.H88 D43 2007 - Main (Gardner) Stacks
Other Books:

Hypatia of Alexandria / Maria Dzielska; translated by F. Lyra
B667.H84 D95 1995 - Main (Gardner) Stacks

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Hypatia of Alexandria Greek mathematician, astronomer, and philosopher in 4th & 5th century Egypt, recognized for her commentaries on prominent mathematical works of her time Book on Display: Hypatia of Alexandria : mathematician and martyr / Michael A.B. Deakin QA29.H88 D43 2007 - Main (Gardner) Stacks Other Books: Hypatia of Alexandria / Maria Dzielska; translated by F.